A gamma integral

1. Apr 7, 2012

mmzaj

greetings . any ideas on how to evaluate this integral

$$\lim_{T\rightarrow \infty}\frac{1}{2T}\int_{-T}^{T}\frac{\Gamma(3+it)}{\Gamma(3+it-j)}e^{ikt}dt$$

$j, k$ are positive constants .

2. Apr 8, 2012

JJacquelin

Hi !
this integral cannot be evaluated for T-->infinity because it is not convergent.

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3. Apr 8, 2012

mathman

The gamma function ratio is a polynomial in t (degree = j, if j is an integer).

4. Apr 8, 2012

KarmonEuloid

Not sure, but would a fourier transform help here?

5. Apr 9, 2012

JJacquelin

I don't think so. Since the integral is not convergent for T tending to infinity, the Fourier transform is of no help to find a limit which doesn't exist anyways.

This is a so-called Pochhammer polynomial.